Question

If a circle passes through the point $(0,0),(a,0)$ and $(0,b)$ then find the coordinates of its centre.

Answer 1

From diagram, it is clear that $PQ$ chord make right angle at origin.

Where $P\equiv (a,0)$ and $Q\equiv (0,b)$

$\therefore PQ$ is diameter of given circle and midpoint of $PQ$ i.e. $C$ represent the centre of the circle.

$\therefore Center,C=(\frac{a+0}{2},\frac{0+b}{2})=(\frac{a}{2},\frac{b}{2})$

Hence, the coordinates of center of circle is $(\frac{a}{2},\frac{b}{2})$